A Polyhedral Off-Line Robust MPC Strategy for Uncertain Polytopic Discrete-Time Systems

In this paper, an off-line synthesis approach to robust constrained model predictive control for uncertain polytopic discrete-time systems is presented. Most of the computational burdens are moved off-line by pre-computing a sequence of state feedback control laws that corresponds to a sequence of polyhedral invariant sets. The state feedback control laws computed are derived by minimizing the nominal performance cost in order to improve control performance. At each sampling instant, the smallest polyhedral invariant set containing the currently measured state is determined. The corresponding state feedback control law is then implemented to the process. The controller design is illustrated with two examples in chemical processes. The proposed algorithm is compared with an ellipsoidal off-line robust model predictive control algorithm derived by minimizing the worst-case performance cost and an ellipsoidal off-line robust model predictive control algorithm derived by minimizing the nominal performance cost. The results show that the proposed algorithm can achieve better control performance. Moreover, a significantly larger stabilizable region is obtained

Constrained MPC for uncertain linear systems with ellipsoidal target sets

Robustly feasible invariant sets provide a way of identifying stabilizable regions for uncertain/time-varying linear systems with input constraints under fixed state feedback control laws. With the introduction of extra degrees of freedom in the form of perturbed control laws, these stabilizable regions can be enlarged. This was done in Lee and Kouvaritakis (Automatica 36 (2000) 1497-1504) in conjunction with polyhedral invariant sets and the aim here is to extend this work using ellipsoidal target sets. We also extend the analysis to take into account both polytopic and unstructured bounded disturbances, as well as unstructured uncertainties. © Elsevier Science B.V. All rights reserved